Rice and Grealish – who have both represented Ireland in the past – were the target of loud boos and jeers from minute one at the Aviva Stadium but it appeared to give the duo extra motivation to perform.
And while some England fans began calling for Carsley to be handed the job on a permanent basis as Grealish increased the deficit in the 26th minute, it was a far more reserved showing from the visitors in the second period.
But Carsley will undoubtedly be pleased to get maximum points on the board and the 50-year-old will be desperate to make it two wins from two when the Three Lions entertain Finland at Wembley on Tuesday night.
Former Ireland and Manchester United captain Keane was impressed with England’s display before the break but slammed their efforts in the second half as the hosts managed to keep their chances to a minimum.
‘The frustrating thing for England today was that Ireland were there for the taking,’ Keane said on ITV.
‘England dominated in the first half, we praised them and their decision-making, their quality, their movement.
‘But that was the opposite in the second half. I thought they were awful in the second half, players playing for themselves, taking too many touches, trying to play Roy of the Rovers passes.
‘Keep doing the basics and suck Ireland out. But Ireland played with a lot of pride in the second half.
‘But as good as England were in the first half, I thought they were just as bad in the second half. Players playing for themselves.
‘Even the substitutions… players strolling off, showing a bit of arrogance.
‘If there’s a team there for the taking, especially the attacking players… if you’re on that pitch you’re thinking, “I’ve got chances there to go and score a goal!”.’
Ian Wright, meanwhile, accused England’s players of easing off when they should have been ‘pressing it home’ in the second period.
‘It felt to me like they took their foot off the gas a bit, maybe because Ireland didn’t come at them as I thought they would, a bit more positive,’ the ex-England and Arsenal forward said.
‘I thought [Chiedozie] Ogbene did really well for them, he tried. I’d like to have seen [Evan] Ferguson come on earlier, maybe he’s got an injury.
‘But from England’s point of view, the way we started and the way we played, I thought we should have pressed it home a little bit more, started with the same intensity to see if we could get three or four. Just play the game that way, a little more ruthless.’
Speaking to ITV shortly after the final whistle, Carsley praised his players and felt they deserved ‘all of the credit’ for the win.
‘I thought it was good in parts. I think you’ve seen some of the things that we’ve tried to do,’ Carlsey said.
‘The lads have got to take a lot of credit, well all of the credit. I think we’ve shown that we have some real talent.
‘We can be really pleased with the clean sheet as well.’
On Rice and Grealish’s strikes, the England caretaker boss added: ‘I thought they both took their goals really well, really well-worked moves and brilliant finishes.
‘I think they can both, moving forward, score a lot more goals and add goals to their game.’